Ricci flow does not preserve positive sectional curvature in dimension four

Abstract

We find examples of cohomogeneity one metrics on $S^4$ and $\mathbb{C}{P}^2$ with positive sectional curvature that lose this property when evolved via Ricci flow. These metrics are arbitrarily small perturbations of Grove--Ziller metrics with flat planes that become instantly negatively curved under Ricci flow.

LaTeX2e, 18 pages, 2 figures

Cited by in corpus (1)

• Extremality and rigidity for scalar curvature in dimension four